This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Teacher perception is one of the most important factors determining classroom teaching practices. Multiple representations are used extensively in mathematics classrooms, especially in developing conceptual understanding. The data in this study, which aims to compare Turkish and US middle school mathematics teachers' perceptions of multiple…

In 2024, the National Center for Education Statistics (NCES) administered the National Assessment of Educational Progress (NAEP) mathematics assessment to representative samples of fourth- and eighth-grade students in the nation, states, the District of Columbia, Puerto Rico, Department of Defense schools, and 26 participating large urban…

Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical…

Digital learning games have been increasingly adopted in classrooms to facilitate learning and to promote learning outcomes. Contrary to common beliefs, many digital learning games can be more effective for female students than male students in terms of learning and affective outcomes. However, the in-game learning mechanisms that explain these…

The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

Computational thinking (CT) competency is essential for K-12 students in the digital societies. Understanding the relationship between students' CT and relevant factors contributes to implementing and improving CT education. Most previous studies investigated the effect of demographic or attitudinal factors on CT performance; whereas few research…

This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with…

Open-ended learning environments (OELEs) support constructivist approaches to STEM learning. This promotes student engagement and facilitates a deeper understanding of STEM topics. Despite their benefits, OELEs can present significant challenges for novice learners. Recent studies have revealed the complex relationship between students' affective…

The use of digital technologies in teaching and learning processes has opened new and wide frontiers in mathematics education. Research in education moves towards teaching and learning (and assessing) twenty-first-century skills and computer-based testing seems an interesting possibility for assessing such skills. From this perspective, comparing…

Computational Thinking (CT) skills are increasingly recognized as essential for junior high school students, especially in addressing the demands of the digital era. This study explores how CT skills--decomposition, pattern recognition, abstraction, and algorithmic thinking--manifest in learning statistics based on students' cognitive abilities. A…

Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant…

Problem-solving ability was one of the competencies that students had to have, but it became more important when learning mathematics. Quite a lot of research has studied this ability, but not much has studied how to optimise it, especially using didactical design research based on lesson study. Participants in this research were 10 students…

In this study, we aimed to investigate the impact of cooperative learning on the computational thinking skills and academic performances of middle school students in the computational problem-solving approach. We used the pretest-posttest control group design of the quasiexperimental method. In the research, computational problem-solving…